Find All Complex Solutions 8e^x-5=0

$8 e^{x} - 5 = 0$

Add $5$ to both sides of the equation.

$8 e^{x} = 5$

Divide each term in $8 e^{x} = 5$ by $8$ and simplify.

Divide each term in $8 e^{x} = 5$ by $8$ .

$\frac{8 e^{x}}{8} = \frac{5}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 e^{x}}{8} = \frac{5}{8}$

Divide $e^{x}$ by $1$ .

$e^{x} = \frac{5}{8}$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{x}) = \ln (\frac{5}{8})$

Expand the left side.

Expand $\ln (e^{x})$ by moving $x$ outside the logarithm.

$x \ln (e) = \ln (\frac{5}{8})$

The natural logarithm of $e$ is $1$ .

$x \cdot 1 = \ln (\frac{5}{8})$

Multiply $x$ by $1$ .

$x = \ln (\frac{5}{8})$